MGMT2263

Worksheet #2

 

1)     For the following scenarios, state whether the samples are dependent or independent.

a)     Two colleges wanted to compare the mean SAT scores on their incoming freshmen. One college gathered 98 scores and the other took a sample of 52 scores.

b)     A retail store would like to compare sales from two different arrangements of displaying its merchandise. Sales are recorded for a 30-day period with one arrangement and then sales are recorded for another 30-day period for the alternative arrangement.

c)     Fifty people were randomly selected to rate Coke and Pepsi on a scale from 1 to 10 and the ratings were compared.

(a and b: independent, c: dependent)

2)     For each of the following scenarios state which test to conduct. Choose from Z-test, t-test assuming equal variances, t-test assuming unequal variances, paired t-test, Mann-Whitney test or Wilcoxon test.

a)     A survey is conducted in Calgary and Edmonton to see if there is any significant difference in the average amount people spend eating out. They pull equal sample sizes of 200 for each city.

b)     A teacher wanted to compare marks between her two classes. She has 25 students in one class and 28 in the other. When she checked to see if the data was normally distributed, she found that the marks for both classes were heavily skewed left.

c)     A store did a shopper-intercept survey in a mall asking 100 people to rate 2 new logos on a scale from 1 to 5, 5 being best.

d)     A store wanted to compare average daily sales at 2 of its locations. They took samples of 10 daily sales from both stores (the dates were independently chosen for each store). Analysis indicated the standard deviations were equal and that the data followed a normal distribution.

e)     A store ran an identical ad campaign at 2 of its locations. It then sampled the same 10 days of data from both stores in order to compare average sales between the stores. Analysis indicated the data followed a normal distribution.

(a: Z test; b: Mann-Whitney; c: Wilcoxon; d: t-test assuming equal variances; e: paired t-test)

3)     A video chain had to choose between 2 locations for its new store. It decided to base its decision on the average number of videos per month watched per household. It surveyed 100 households in the neighbourhood of each location. The results were:

 

Mean

Std. Dec.

Location A

4.4

1.6

Location B

5.6

2.3

Do the residents in location B watch significantly more videos than those in location A on average? Test at a 5% level of significance. (Z = 4.28; residents in location B watch more videos on average)

4)     Is there a level of significance between 1% and 10% in which the opposite verdict would have been reached? (p-value = 0; the answer is no)

5)     Construct a 95% confidence interval of the difference between location B and location A. (0.65 < mB - mA < 1.75)

6)     Suppose they wanted to test the hypothesis that the difference in the average number of videos rented per month between the residents in location B and those in Location A is more than 1 per month. What would the conclusion be? (Z = 0.7138; conclude the difference is not more than 1 per month)

7)     A researcher wanted to determine if there is any significant difference between executives and regular workers in the average number of hours spent tending to emails, text messages, etc. For a random sample of 150 executives, the average per week was 13.5 hours with a standard deviation of  2.4 hours. For a random sample of 200 regular workers, the average per week was 11.5 hours with a standard deviation of 4.5 hours. Test at a 5% level of significance. (Z = 5.35; conclude there is a significant difference)

8)     Construct a 95% confidence interval in the average difference between executives and regular workers in the average time on email, etc., converting the limits to the nearest minute. Interpret the interval. If this interval were used to test the hypothesis in question 7, why would the same conclusion be reached?

(76 < m1 - m2 < 164; hypothesis difference of zero lies outside the interval)

9)     Suppose a level of significance had not been chosen for the hypothesis in question 7. Why would the same conclusion be reached? (p-value < 1%)

10) What would be the appropriate one-tail test? What would be the conclusion? (executives spend significantly more time on email, etc. than regular workers)